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Forces

Area under a velocity-time graph, and the uniform acceleration equation

  • 3 things to know
  • Physics Paper 2

Overview

When the equation linking final velocity, initial velocity, acceleration and distance applies, the equation in words and in the symbols v, u, a and s with its units and calculations, free fall at 9.8 m/s² and the speed of a dropped stone, and how an object falling through a fluid reaches terminal velocity as the resultant force becomes zero.

What you need to know

Answer each one before you reveal it.

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Key term

State in words the equation linking final velocity, initial velocity, acceleration and distance for uniform acceleration.

Key term

Write the uniform acceleration equation using the symbols v, u, a and s.

Numbers

A car starts from rest and accelerates uniformly at 2 m/s² over a distance of 100 m. Calculate its final velocity.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    To what kind of motion does the equation linking final velocity, initial velocity, acceleration and distance apply?

    Model answer

    It applies only to motion with uniform, that is constant, acceleration.

  2. 2

    State in words the equation linking final velocity, initial velocity, acceleration and distance for uniform acceleration.

    Model answer

    Final velocity squared minus initial velocity squared = 2 × acceleration × distance.

  3. 3

    Write the uniform acceleration equation using the symbols v, u, a and s.

    Model answer

    v² − u² = 2as.

  4. 4

    A car starts from rest and accelerates uniformly at 2 m/s² over a distance of 100 m. Calculate its final velocity.

    Model answer

    The final velocity is 20 m/s, because v² = 2 × 2 m/s² × 100 m = 400.

  5. 5

    A train travelling at 30 m/s decelerates uniformly at 0.5 m/s² over 500 m. Calculate its velocity at the end of that distance.

    Model answer

    Its velocity is 20 m/s, because v² = 900 − 2 × 0.5 m/s² × 500 m = 400.

  6. 6

    In the uniform acceleration equation, what does the symbol v stand for and in what unit is it measured?

    Model answer

    v is the final velocity, measured in metres per second, m/s.

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